On Turing dynamical systems and the Atiyah problem

Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental l^2-Betti number with respect to an action of the threefold direct product of the lamplighter group Z/2 wr Z. The main new idea is embedding Turing machines into integral group rings. The main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio

Orbit equivalence rigidity for ergodic actions of the mapping class group

We establish orbit equivalence rigidity for any ergodic, essentially free and measure-preserving action on a standard Borel space with a finite positive measure of the mapping class group for a compact orientable surface with higher complexity. We prove similar rigidity results for a finite direct product of mapping class groups as well.Comment: 11 pages, title changed, a part of contents remove

ION ACCELERATION THROUGH A MAGNETIC BARRIER SINGLE STAGE AND DOUBLE STAGE HALL THRUSTER

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ID-HALL, a new double stage Hall thruster design. I. Principle and hybrid model of ID-HALL

International audienceIn Hall thrusters, ions are extracted from a quasineutral plasma by the electric field induced by the local drop of electron conductivity associated with the presence of a magnetic barrier. Since the electric field is used both to extract and accelerate ions and to generate the plasma, thrust and specific impulse are not independent in a Hall thruster. There is a need for versatile thrusters that can be used for a variety of maneuvers, i.e., that can operate either at high thrust or at high specific impulse for a given power. The double stage Hall thruster (DSHT) design could allow a separate control of ionization and acceleration, and hence separate control of thrust and specific impulse. In the DSHT configuration, a supplementary plasma source (ionization stage), independent of the applied voltage, is added and placed upstream of the magnetic barrier (acceleration stage). The DSHT concept is also well adapted to the use of alternative propellants, lighter and with a less efficient ionization than xenon. Several designs of double stage Hall thrusters have been proposed in the past, but these attempts were not really successful. In this paper, we present a brief review of the main DSHT designs described in the literature, we discuss the relevance of the DSHT concept, and, on the basis of simple physics arguments and simulation results, we propose a new design, called ID-HALL (Inductive Double stage HALL thruster). In this design, the ionization stage is a magnetized inductively coupled RF plasma. The inductive coil is inside the central cylinder of the thruster and located nearby the acceleration stage. Preliminary modeling results of this DSHT are described. Published by AIP Publishing. https://doi

Plate tectonics drive tropical reef biodiversity dynamics

The Cretaceous breakup of Gondwana strongly modified the global distribution of shallow tropical seas reshaping the geographic configuration of marine basins. However, the links between tropical reef availability, plate tectonic processes and marine biodiversity distribution patterns are still unknown. Here, we show that a spatial diversification model constrained by absolute plate motions for the past 140 million years predicts the emergence and movement of diversity hotspots on tropical reefs. The spatial dynamics of tropical reefs explains marine fauna diversification in the Tethyan Ocean during the Cretaceous and early Cenozoic, and identifies an eastward movement of ancestral marine lineages towards the Indo-Australian Archipelago in the Miocene. A mechanistic model based only on habitat-driven diversification and dispersal yields realistic predictions of current biodiversity patterns for both corals and fishes. As in terrestrial systems, we demonstrate that plate tectonics played a major role in driving tropical marine shallow reef biodiversity dynamics

To respond or not to respond - a personal perspective of intestinal tolerance

For many years, the intestine was one of the poor relations of the immunology world, being a realm inhabited mostly by specialists and those interested in unusual phenomena. However, this has changed dramatically in recent years with the realization of how important the microbiota is in shaping immune function throughout the body, and almost every major immunology institution now includes the intestine as an area of interest. One of the most important aspects of the intestinal immune system is how it discriminates carefully between harmless and harmful antigens, in particular, its ability to generate active tolerance to materials such as commensal bacteria and food proteins. This phenomenon has been recognized for more than 100 years, and it is essential for preventing inflammatory disease in the intestine, but its basis remains enigmatic. Here, I discuss the progress that has been made in understanding oral tolerance during my 40 years in the field and highlight the topics that will be the focus of future research

Phase Transitions on Nonamenable Graphs

We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees

Intersection form, laminations and currents on free groups

Let $F_N$ be a free group of rank $N\ge 2$, let $\mu$ be a geodesic current on $F_N$ and let $T$ be an $\mathbb R$-tree with a very small isometric action of $F_N$. We prove that the geometric intersection number $$ is equal to zero if and only if the support of $\mu$ is contained in the dual algebraic lamination $L^2(T)$ of $T$. Applying this result, we obtain a generalization of a theorem of Francaviglia regarding length spectrum compactness for currents with full support. As another application, we define the notion of a \emph{filling} element in $F_N$ and prove that filling elements are "nearly generic" in $F_N$. We also apply our results to the notion of \emph{bounded translation equivalence} in free groups.Comment: revised version, to appear in GAF